VoZ. 2, No. 3, June, 1963
ELECTRICAL AND MAGNETIC PROPERTIES OF TUNGSTEN BRONZES485 CONTRIBUTION FROM
THE BAKERLABORATORY OF CHEMISTRY, CORNELL UNIVERSITY, ITHACA, NEWYORK
Electrical and Magnetic Properties of Potassium Tungsten Bronze and Rubidium Tungsten Bronze’ BY M. J. S I E N K O
AND
SHEILA MAcENNESS MOREHOUSE
Received September 22, 1962 Single crystal conductivities have been measured for KO40W03and Rbo 32WO3 in the range 150 to 370°K. Carrier mobilities, which are somewhat higher than in the Li and Na tungsten bronzes, closely follow a T sinh2 ( 0 / 2 T )dependence. Calculations on the basis of the theory of Howarth and Sondheimer strongly support the assumption that the thermal part of the carrier mobility in the tungsten bronzes is primarily determined by polar scattering from optical mode lattice vibrations Magnetic susceptibilities also have been measured at room temperature for Rbo 26WOa and KO23-0 raWOs. Results are as predicted by the Pauli-Peierls theory for quasi-free electrons.
The tungsten bronzes, MxW03 (0 < x < 1))which have metallic properties2 over a wide range of composition, hold considerable promise as model systems for examining theories of metallic binding. I n particular, the course of a density-of-states function characteristic of a conducting d-band seems directly accessible experimentally as a function of varying electron concentration. However, except for the cubic sodium and lithium tungsten bronzes, for which considerable data exist3 on structure, conductivity, magnetic susceptibility, thermal e.m.f ., and Hall voltage, observations on the other alkali tungsten bronzes are fragmentary, qualitative, and occasionally contradictory. In anticipation of shortly having band calculations for the tungsten bronzes, we have undertaken this investigation of potassium and of rubidium tungsten bronzes to provide parameters for typical non-cubic bronzes. Potassium tungsten bronzes first were prepared by Laurent4 by reduction of K2WOpW03 mixtures with hydrogen. Subsequent preparation methods included reduction of K2W04-WO3 with tin,5 electrolysis of fused K Z W O ~reduction ,~ of KzW04-WO3 with W02,7 and reduction of KzW04-WO3 with elemental tungsten.8 Schaefergwas first to prepare a defined rubidium tungsten bronze by reduction of Rb2C03-H2W04 mixtures with methane and hydrogen. The potassium bronzes, K,W03, have been found to be tetragonal in the ranges>’O0.40 < x < 0.57, with a = 12.285 A.and c = 3.833 A.a t x = 0.48, expanding to a = 12.317 and c = 3.841 A.a t x = 0.57. In the range 0,27 < x < 0.31 they are hexagona1,lI with a = 7.40 and c =
A.
A.
(1) This research was supported by the Air Force Office of Scientific Research under Contract No AF49(638)-191 and by the Advanced Research Projects Agency (2) L D Ellerbeck, H R Shanks, P H Sidles, and G C Danielson, J Chem Phys , 35, 298 (1961) (3) G Hagg, Z physzk Chem., B29, 192 (1935), B W Brown and E Banks, Phys Rev,84, fiO9 (1951), L E Conroy and M J Sienko, J A m Chem Soc , 1 4 , 3520 (1952), W R Gardner and G C Danielson, Phys R e v , 93, 46 (1954) (4) A Lament, A n n chtm phys , [21 67, 215 (1838) (5) G von Knorre, J p i a k l Chem , [21 27, 49 (1883). (6) E Zettnow, Pogg A n n , 130, 240 (1867) (7) 0 Brunner, Dissertation, Zurich, 1903 (8) E 0 Brimm, J C Brantley, J H Lorenz, and M H Jellinek, J A m Chem Soc , 1 3 , 5427 (1951) (9) E Schaefer, Z anorg aZZgem Chem , 38, 158 (1904) (10) A Magnkli, Arkm Xemz, 1, 213 (1949) ( 1 1 ) A. Nagndli, A c f u Clzem. Scund., I , 315 (1963).
7.56 A.a t x = 0.27, contracting to a = 7.37 A.and c = 7.54 A.a t x = 0.31. In the range 0.27 < x < 0.29, the rubidium tungsten bronies Rb,WO3 are isomorphous with the hexagonal potassium bronzes. Magneli’s detailed structural studiesll on Rbo 29W03 indicate six formula units of Rb,W03 per unit cell, a = 7.38 fi. and c = 7.56 A.,with the WO6 octahedra connected by common corners to form a regular network of 3- and 6membered rings arranged in layers normal to the hexagonal axis. Conductivity data presently available on K,W03 and Rb,wOa are limited to room temperature measurements on pressed powder samples. Straumanis and co-workers reportl2 a specific resistivity of 1.3 X ohm cm. for K0.54W03 increasing with lowered K content to about 5 X ohm cm. for K O . ~ O W OMag~. n6lill reports 5 X ohm cm. for Ko.27--0.31W03and 3 X lop2 ohm ’cm. for Rb0.27-0.29W03. These values represent upper limits, as usually is true for powder studies, but they seem orders of magnitude too high t o be consistent with the obvious metallic appearance of the materials. Furthermore, resistivities of this order would require considerable modification in the total ionization model applicable to Na,W03 and Li,WO3.I3 A major effort in this research was to prepare single crystals of K,W03 and Rb,WO3 so that bulk resistivities could be determined without grain contact effects such as probably are present in the above work. So far as magnetic studies are concerned, there are no available data on Rb,W03 and two fragmentary sets on K,W03. Stubbin and MellorI4reported 50 X l o p 6 and 30 X lov6 for the molar susceptibilities a t room temperature of KO63W03 and Ko.67W03, respectively, with no detectable change over the temperature range 300457’K. Kupka and Sienko15found a t 294’K. a molar susceptibility of 100 X for KOb3W03. Both sets of results were interpreted as being consistent with a free-electron model. (12) M. E. Straumanis, S. C. das Gupta, and C. H . Ma, Z . anoug. Chem., 265, 209 (1951). (13) M. J. Sienko and T. B. N. Truong, J . A m . Chem. Soc., 83, 3939 (1961). (14) P. M. Stubbin and D. P. Mellor, Pvor. Roy. Soc. N.S. Wales, $2, 225 (1948). (15) F. Kupka and M. f . Sienko, d , Chem, Phy?., 18, 1296 (1950),
AND 486 M. J. SIENKO
E
-* -I I-
'I
l
S.RT. MOREHOUSE
Inorganic Clzemistry
/-
I
J' //
I
/
'
! *' I50
Rb0.32W03
A
200
250
0.4OW03
300
TEMPERATURE
350
O K
Fig. l.-Observed resistivity as a function of temperature for typical single crystals of rubidium and potassium tungsten bronzes.
Experimental Preparation of Materials.-Single crystals of K,W03 were prepared by electrolytic decomposition of melts resulting from fusion of 1 : 2 molar ratios of KpCO~'1v03in a Selas crucible i n side a porcelain crucible. Tungsten rod (2.5 mm. diameter) in the center unit served as cathode; platinum wire (1.8 mm.) between the walls of the crucibles, as anode. While the cell was heated to 800' in a n electric furnace t h a t was continually flushed with argon, electrolysis current was passed through the melt from a 6-volt storage battery for about 5 . 5 hr. Voltage drop between the electrodes was 1.1 volts; current remained constant at 30 ma. The product, after purification, consisted of rather well formed red crystals, the largest of which were from 8 to 10 mm. long and 1 mm. square. Useable single crystals of Rb,WOJ could not be prepared in the above unit because of impaction in the Selas frit. Large crystalline aggregates were readily made by electrolysis in a Vycor Ucell from which the melt could be poured away from the product, but the individual crystals were poorly formed, probably because of too rapid growth. T h e best crystals were obtained in a cell consisting simply of a platinum rod cathode centered in a platinum crucible which served as anode. After 3 hr. of electrolysis at 800' under argon, using 18 ma at 1.0 volt, radial clusters of bronze crystals adhering to the cathode could be lifted out of the melt, cooled, and leached successively in HzO, NH3, 57, NanCOJ, and HF. Remarkably perfect hexagonal prisms were obtained up to 6 mm. long and 2 mm. on hexagonal edge. Because of the possibility of occluding tungstate melt, great care had to be taken to ensure homogeneity of the crystals used for the electrical measurements. Results were considered admissible only if consistent for several probe settings and for different faces of the crystal and if the crystal could be cleaved repeatedly after the measurements were completed without disclosing signs of occlusion. For the magnetic studies, where powder samples were preferred,
K,WOa and Rb,WOa both were made by heating intimately ground rnixturcs o f alkali carbonate, Vi 01,and W to about 750' in an evacuated combustion tube For periods of 10 to 24 hr. As with the sirigle crystals, all of the products were purified by successive leaching with boiling water, hot dilute aqueous KH.,, boiling 57; Sa2C08,and 4896 HF. The N a 2 C 0 3was used sparingly because it alone of these reagents appreciably attacks the bronzes. Samples were used for magnetic measurements only if X-ray examination indicated homogeneous bronze composition. Chemical Analysis.-The bronzes were decomposed by fusion in a 3: 1 by weight mixture of h-aNOa and iYazCO8. Potassium and rubidium were determined by flame photometry using spectral lines at 767 and 794.8 mp for K and R b , respectively. Because the phototube was not so sensitive in the R b region, the R b bronzes also were analyzed by a gravimetric techniqueI6 depending on conversion of Rb,WO3 to RbCl by oxidation in an HCI-02 stream. A third method of alkali determination was by difference, using tungsten analysis to compute \%'OS which then was subtracted from M,WO,. The tungsten method and the HCI method agreed with each other to 3 % ; they corresponded to the flame photometer method within lOy0 of the alkali content. The tungsten analysis was performed by HgWOd precipitation with cinchonine scavenging followed by ignition to R703. Density Determination.-Single crystal densities were determined pycnometrically using water as immersion liquid. Results, which are appreciably different from those previously reported," the new ones being closer to the X-ray computed values, are given in Table I along with the X-ray spacings observed. XR a y powder photographs were taken on ground-up single crystals in a 114.60-mm. camera with CuKa radiation.
TABLE I STRUCTURE PARAMETERS OF K Composition
Rbo.82WC3 Ko.aW03
AND
R b BROSZES
Density, g /cc.
Symmetry
7 16 f 0 04 7 18 zt 0 03
Hexagonal Tetragonal
a,
A,
c,
7.386 12 25
A.
7.54 2 81
Electrical Measurements .-JVell shaped crystals were mounted for potential probe measurement, essentially as previously described,I7 in a soapstone holder with adjustable copper current leads and spring loaded brass probes. Indium inserts between crystal and current leads reduced contact resistance t o less than 0.1 ohm. The holder and probe assembly was mounted in a Vycor tube which was evacuated or filled with argon. Temperature variation was produced by a n electric furnace or by immersion in a dewar filled with various cryogenic mixtures. Potential difference between the sensing probes was measured with a Leeds and Sorthrup Type K3 potentiometer. Current through the crystal, periodically reversed t o compensate for thermoelectric effects, was monitored by measuring IR drop through a standard resistance in series with the crystal. Figure 1 shows observed resistivities as a function of temperature for two specific crystals. Table I1 gives values averaged over several crystals from the same electrolytic preparation. Because the growth habit favors elongation in the c-direction, these values correspond to resistivity parallel to the c-axis. Magnetic Measurements.-Magnetic susceptibilities of the rubidium and potassium bronzes were measured by the Gouy
TABLE I1 ELECTRICAL RESISTIVITIES OF K ASD R b BRONZES AT 25' Composition
Rbo ?zwo3 KOaoWOs
Resistivity ohm cm.
p,
( 6 32 f 0 9) X 10-6 ( 3 82 f 0 4 ) X 10@
Thermal coefficient I / Pdp/dT
4 G 4 5
x x
10-3 10-3
(16) A. MagnCli, Arkio Kenii, 1, 273 (1919). (17) M . J. Sienko and P. F. Weller, Inoug. Chern., 1, 324 (1862)
ELECTRICAL AND MAGNETIC PROPERTIES OF TUNGSTEN BRONZES 487
Vol. 2, No. 3, June, 1963
method using the electromagnet and procedure previously described." Freshly boiled, doubly distilled water was used as standard. Packing densities of the bronzes for converting measured apparent volume susceptibilities to mass susceptibilities were obtained via cathetometric measurement of powder sample dimensions as contained in the precision-bore Pyrex sample tubes. Each sample was measured a t three independent packings; each packing, a t five separate alignments in the magnetic field. Table I11 gives the observed susceptibilities for various bronze compositions per gram, x, and per gram-formula, xy, as well as the per cent deviation in the measured values. All measurements were performed a t room temperature as monitored in the nitrogen-containing lucite box which isolated the sample from the surroundings. There were no detectable changes in susceptibility as room temperature varied between 24 and 28".
C; 1.7al
Y
3
"5 1.6a
1.5
-
o 1.4 I
-
2.
-
I-
4
m
\
\
0
0
TABLE I11 Composition
Rbo.zaW03
KOz3wo3 KO. z gWO3 Ko.3oW03 K0.45W03
X,
X I
susceptibility per g.
susceptibility per mole
-5.52 x lo-' -3.62 X lo-' -1.74 x lo-' -1.89 X 9.82 x lo-'
-1.40 -8.71 -4 32 -4.60 24.5
1.3-
3
'.
% deviation
x
3
X lo-' X lo-' X lo-' X
6 4
1.21
2 3
Discussion For both the potassium and the rubidium tungsten bronzes the conductivity is very high, being some three orders of magnitude greater than the values previously reported by Straumanislz and Magndi.ll Furthermore, a t least in the range studied, between 150 and 350°K., behavior is metallic in that resistivity is almost linear with temperature. Assuming that the K and the Rb in M,W03 are completely dissociated into cations and free electrons, the carrier mobility p can be calculated from CT = n e p , where u is the observed specific conductivity and n is the number of carriers per cc. As shown in Fig. 2, for Rb0.32W03,p decreases from 55.9 cm.2/ volt sec. a t -120' to 14.3 a t 90'; for Ko.40W03, from 66.1 to 18.1 cm.2/volt sec. The curve for Rb~.~2W03 corresponds to a T-lsV6dependence a t low temperature and a T-1.35 dependence a t high: for K0.40W03, to T-le61 and T - l e 3 0 , respectively. These functions are close to the P 3 I 2 predicted theoretically for lattice scattering. l9 The carrier mobilities calculated on the assumption of total ionization of Rb and K are of the same order of magnitude as those found for sodium tungsten and lithium tungsten bronzes.13 The inference is that the same band of delocalized molecular orbitals produced by overlap of 5d (tz,) tungsten orbitals, used to account for the metallic properties of Na and Li W bronzes, also provides the mechanism of electrical transport in the K and Rb W bronzes. The fact that the observed mobilities in the K and R b bronzes are somewhat higher than those in Li and Na bronzes a t the same temperature and alkali content may be a result of anisotropy in the structure of the hexagonal and tetragonal bronzes, the resistivity results given above representing mobili(18) J. L. Kernahan and M. J. Sienko, J . A m . Chem. Soc., 11, 1978 (1955). (19) J. Bardeen and W Shockley, Phys R e a , SO, 72 (1960)
2.1
2.2
2.4
2.3 Log T
2.5
2.6
O K
Fig. 2.-Logarithmic plot of carrier mobility vs. temperature for single crystals of rubidium and potassium tungsten bronzes.
ties parallel to the c-axis. Measurements made on a single crystal of Rbo.32WO3, which accidentally grew as a thin plate of large extension in the ab-plane, gave a t room temperature a significantly higher resistivity (4 X ohm-cm., perpendicular to the c-axis, compared to 6.3 X ohm-cm. parallel to c). Nevertheless there is no correlation between increased carrier mobility and decreased spacing between W atoms, as might be nalvely predicted from a 5d overlap model. In fact, with the exception of the sodium case, data summarized in Table I V suggest decreased carrier mobility with decreased W-W spacing. However, because i t is difficult to attain experimentally full values of the mobility, influences such as defects acting to reduce the true value, mobility comparisons between different substances have to be made with extreme caution. If the comparison indicated by Table IV is supported by independent measurements, then before significance is attached to it, the resistivity measureTABLE IV Composition
Structure
P,
Nearest
cm.l/volt sec.
It.
w-w,
Lio.siWOa
Cubic
6.1-9.3
3 72
Nao.raWOa
Cubic
4.0
3.81
Ko.aoWOa Rho.azWOa
Tetragonal Hexagonal
(11
23.4 to c) 1 8 . 5 ( to c) 3 . 3 (Iloc)
3.70
(Ito c)
Reference SienkoTruongls McNeillConroyzo This work This work This work
(20) W. McNeill and L. E. Conroy, J . Chem. Phys., 36, 87 (1902).
488 M. J. SIENKO AND S. M. MOREHOUSE ments need to be extended to lower temperature so that the “residual resistivity” can be corrected for. Also, Hall measurements need to be done to give a direct measure of carrier concentration, something which has been done only for the Li and the Na bronzes. In connection with carrier studies in the y phase of W03, Crowder and SienkoZ1have found that the electrical resistivity and the thermal e x ” . of n-type W03 can be explained quantitatively by assuming that the thermally dependent part of the carrier motion is limited primarily by polar scattering from optical mode lattice vibrations. Using three parameters to describe the interaction between the electron and the lattice-viz., an optical mode characteristic temperature of 600°K., a static dielectric constant of approximately 1000, and an optical frequency dielectric constant of 6.2-they were able to compute optical contributions to the resistivity which satisfactorily reproduce not only the dependence of conductivity and thermal e.m.f. on temperature but also the change of these variables as a function of the composition parameter x in Na,W03. Assuming that the same conduction process is operative in Rb,W03 and K,WOa as in Na,WO&.e., ignoring anisotropy-it is possible to extend the above calculations to these bronzes. For this purpose, the total resistivity, p, is defined as the sum of a residual part, pa, which results from neutral impurity or defect scattering, and a thermal part, popt, which is believed to arise only from optical mode scattering. Acoustical mode scattering, although undoubtedly present, is assumed to contribute a negligible amount. Following the theoretical analysis of Howarth and SondheimerZ2 for electronic conduction in polar semiconductors, the optical part of the resistivity can be written 1 e - = ATEp2 sinh2 2T = UOPt Popt
Inorganic Chemistry +
r
1
where 0 is taken to have the value 6OOOK. (On the basis of heat capacity measurements, Vest, Griffel, and Smithz3reported that the acoustic mode characteristic temperature varied from 454-505 O K . in the range h-ao.56--0.89W03 but rose to 589OK. in Nao.73W03after annealing. CrowderZ4finds the optical mode characteristic temperature to be somewhat higher and that 6 = B O O O K . gives a best fit for the WOa and Na,W03 electrical data.) The Fermi energy, E F )assumed to be constant in the above differentiation, is calculated as for a degenerate electron gasz5
where n is the number of free electrons per cc., h is Planck’s constant, and m is the electronic mass. Assuming that n is equal to the number of M atoms per cc. of Yi,WOs and m is the same as the electronic rest mass, we calculate that the Fermi energy in K0,40W03 is 2.14 X erg (or 1.34 e.v.) and that in Rbo.32WOa, 1.76 X erg (or 1.10 e.v.). Under these assumptions, the constant A becomes 1.54 X (c.g.s.units) in Ko.40W03 and 1.32 X in Rbo.3zW03. In the theory of Howarth and Sondheimer, the constant A has the form (32/3) ( a 3 X k / e 2 h 3 )where , a is the interionic distance in the polar lattice, il/lis the reduced mass of the vibrating ions, k is Boltzmann’s constant, e is the charge, and h is Planck’s constant. A crude estimate of A can be made by equating a to 1.9 X lo-* cm., the observed &-0 distancez6 in WOa and the tungsten bronzes, and setting M equal to the oxygen is remass. The value of A so estimated, 4.1 X markably close to the empirical values quoted above, especially considering that there is probably a high degree of covalence in the WOa network which acts to reduce the effective charges. Table V displays the comparison between the computed and the observed resistivities using the equations
where A is a constant, E F is the Fermi energy, and 0 is a characteristic temperature for the crystal. In the case of Na,W03, resistivity measurements2 have been carried to low enough temperatures that the p os. T curve can be extrapolated to T = 0. This gives po, which can be subtracted from p(T = 300°K.) to give popt(T = 300°K.), hence permitting calculation of A . For Nao 5W03,A so found is 1.23 X l o d 7in c.g.s. units, or 1.37 X loz5in practical units. In the case of Rb,WOa and K,W03, the resistivity measurements have not been taken to low enough temperature to permit direct evaluation of po by extrapolation. Instead, the observed value of the thermal coefficient of p has been used to evaluate popt (and hence A ) a t room temperature. Once popt is known a t a given temperature, it can be used to correct an observed p a t that temperature to disclose p0. The pertinent equations are
for Ko.4oW03 and Rb0.32m70&respectively. As with the lithium tungsten bronzesz7 and the sodium tungsten bronzesl5Szgthe magnetic susceptibility of K,W03 and of Rb,W03 is quite low-much lower than would be predicted for locally bound unpaired electrons such as would pertain to Mo plus WO:i or M+ plus W(V). Qualitatively, the low moments
(21) B. L. Crowder and M J. Sienko, J . Chenz. Phys., in press. (22) D. Howarth and E. Sondheimer, P ~ o c .R o y . SOL. (London), A219, 83 (1953).
(23) R. W. Vest, M. Griffel, and J. F. Smith, J . Chem. Phys., 28, 293 (1958). (24) B. T,. Crowder, private communication. ( 2 3 ) See, for example, X. Cusack, “The Electrical and Magnetic Properlies of Solids,” Longmans, Green, and Co., Kew York, N . Y., 1958, p. 24. (26) For summary, see R . P. Ozerov, U s p . Khim., 24, 951 (1955). (27) L. E. Conroy and hl. J. Sienko, J . A m . Chem. Soc., 74, 3.520 (1952). (28) J. Il. Greiner, H R. Shanks, and D. C. Wallace, J . Chem. Phys., 36, 7 7 2 (19G2).
p
(ohm c m . ) = 0.69 X l o u 5
+
p
(ohm cm.) = 1.00 X 10-E
+ II1.47 X
I-‘
1.71 X 1 0 2 5 T E sinhZ ~2 2T e
1OZ5TEp2 sinhZ2T e I-I
Vol. 2, No. 3, June, 1963
OXIDATION OF
TABLE V ELECTRICAL RESISTIVITIES (pOHM T,
Y-KD.~OWO~Computed Obsd.
OK.
...
6.9 6.9 8.2 13.4 21 .o 29.4 37.9 46.1 54.7
0 50 100 150 200 250 300 350 400
... ... 12.8 21.4 29.6 38.2 46.8
...
CM.)
c--Rbo.azWOs--Computed Obsd.
... ... ...
10.0 10.0 12.2 21.1 34.1 48.6 63 .O 77.0 91.7
20.6 34.8 49.2 64.0 78.4
THINSINGLE CRYSTALS OF
COPPER
489
were carefully purified by multiple reprecipitation techniques.) As given in the table, K,- experimental is the observed magnetic susceptibility per unit volume attributable to the electrons. It is computed by subtracting the appropriate diamagnetic corrections for M + and WOa from the observed susceptibility and dividing the difference by the molar volume of the bronze. The values given for K,- theoretical are computed from the Pauli-Peierls equation30
...
TABLE VI
can be explained by having a delocalized spin system as would exist in a conduction band. I n such a case, the magnetic susceptibility can be computed from the quasi-free-electron model following the procedure of Sienko and Truong.13 Table V I summarizes the parameters involved in the computation, assuming diamagnetic contribution^^^ of - 14.6 X per mole of K+, -22.0 X per mole of Rb+, and - 13.0 X lop6 per mole of W03. (The correction for W 0 3was determined by actual measurement on the Fisher “purified tungstic anhydride” from which the bronzes were prepared. As also found by Greiner, Shanks, and Wallace,2sthis material is less diamagnetic than the -21.0 X value reported by Conroy and Sienko. The latter was based on measurements made on Wo3 samples which
using the assumption that the conduction electrons are completely free-that is, that the effective mass of the electrons, m”, is equal to the electronic rest mass, mob To reconcile the observed electronic susceptibility with the theoretical, i t is necessary to assume that the effective mass of the carriers is greater than the rest mass by the amounts shown in the last column of Table VI. Except for the last entry, for K0.46W03, the effective masses for the K and R b tungsten bronzes closely approximate the values characteristic of the Li and Na tungsten bronzes, in spite of the anisotropic character of the former. The unusually high effective mass in Ko.46WOa agrees with the higher susceptibility of K0.6~W03 previously reported by Kupka and Sienko. The break in Table VI between the last and the next-tolast lines coincides with the division between tetragonal and hexagonal structures. The need for further single crystal work to examine any anisotropy in both the conductivity and the magnetic susceptibility is clearly evident. However, the general model for tungsten bronzes in which M interstitials are assumed to have donated electrons to a conduction band of the host WO3 seems to be substantially supported by the above work.
(29) G. W. Brindley and F. E. Hoare, Trans. Favaday Soc., 33, 268 (1937); PYOC. Phys. JOG.(London), 49, 619 (1937).
(30) See, for example, A. H. Wilson, “The Theory of Metals,” 2nd Ed., Cambridge University Press, Cambridge, 1954, p. 155.
MAGNETIC PARAMETERS OF K Xdia
AND
xe-
x
Composition
106 correction
Rbo.neWO3 K0.23W03 KOzgW03 K0.30W03 Ko.46W03
-18.7 -16.3 -17.2 -17.4 -17.6
x
106 exptl.
0.49 .21 .35 .35 1.3
R b TUNGSTEN BRONZES n X 10-21, e-/cc.
4.4
3.8 4.7 4.9 7.8
xe-
x
106 theor.
m*/mo
0.24 .23 .25 .25 .29
1.6 0.9 1.2 1.2 2.9
CONTRIBUTION FROM THE CHEMISTRY DEPARTMENT, UNIVERSITY OF MICHIGAN, ANNARBOR,MICHIGAN
Oxidation of Thin Single Crystals of Copper1 BY R . B. MARCUS
AND
L. 0. BROCKWAY
Received December 10,1962 Single crystal films of copper of 700-800 A. thickness have been prepared in two states: (a) showing many wide stacking faults and few dislocations, and ( b ) showing no stacking faults and a high density of dislocations. On treatment with oxygen gas a t 0.9 p and 525’ cuprous oxide crystals appear with two epitaxial relations to the copper. On the type (a) copper film the oxide particles show some tendency to nucleate along the stacking faults. On both types the oxide growth has a 20-min. incubation period followed by the sudden appearance of oxide grains of 0.5 p diameter which increase in size by twofold in the following 20 min.
Chemical reactions involving a solid phase as one of the reactants are probably as old as chemistry itself, but (1) This work was supported in part by the Atomic Energy Commission under Contract No. AT(11-1)-1086.
only quite recently have the techniques been developed which allow the detailed study of the influence of the physical state of the solid on its chemical behavior. With the techniques of electron microscopy and electron
